text: Consider an infinitely long plate which is oscillating with a velocity  in the  direction, which is located at  in an infinite domain of fluid, where  is the frequency of the oscillations. The incompressible Navier–Stokes equations reduce to
  where  is the kinematic viscosity. The pressure gradient does not enter into the problem. The initial, no-slip condition on the wall is
  and the second boundary condition is due to the fact that the motion at  is not felt at infinity. The flow is only due to the motion of the plate, there is no imposed pressure gradient.